4 papers · 1 filter
The Follow-the-Leader scheme with non-monotone velocity
Marco Di Francesco
This paper addresses the approximation of entropy solutions to a one-dimensional scalar conservation law via the so-called Follow-the-Leader particle scheme in case the velocity ma…
A system of continuity equations with nonlocal interactions of Morse type
Marco Di Francesco, Valeria Iorio
We study a system of two continuity equations with nonlocal velocity fields using interaction potentials of both attractive and repulsive Morse type. Such a system is of interest i…
Measure solutions, smoothing effect, and deterministic particle approximation for a conservation law with nonlocal flux
M. Di Francesco, S. Fagioli, E. Radici
We consider a class of nonlocal conservation laws with an interaction kernel supported on the negative real half-line and featuring a decreasing jump at the origin. We provide, for…
The approximation of the quadratic porous medium equation via nonlocal interacting particles subject to repulsive Morse potential
Marco Di Francesco, Valeria Iorio, Markus Schmidtchen
We propose a deterministic particle method for a one-dimensional nonlocal equation with interactions through the repulsive Morse potential. We show that the particle method converg…